ARTICLE pubs.acs.org/IECR
Mechanistic Modeling of Hydrolysis and Esterification for Biofuel Processes Shujauddin Changi, Tanawan Pinnarat, and Phillip E. Savage* Chemical Engineering Department, University of Michigan, Ann Arbor, Michigan 48109-2136, United States
bS Supporting Information ABSTRACT: We have elucidated the mechanism for ethyl oleate hydrolysis in high temperature water and its reverse reaction, oleic acid esterification in near- and supercritical ethanol in the absence of any other added compounds. Both reactions are acid catalyzed. H+ (from dissociation of water and oleic acid) and oleic acid serve as catalysts for hydrolysis and H+ alone is the catalyst for esterification. The rate equation arising from the proposed mechanism provided a good fit of experimental conversion data for both hydrolysis and esterification. The rate equation accurately predicted the influence of pH on hydrolysis for acidic and near-neutral conditions. The mechanistic model exhibits the ability to make quantitatively accurate predictions within and outside the original parameter space, especially for a multicomponent system. Sensitivity analysis shows that the values of the dissociation constant of oleic acid in ethanol, water, and ethanolwater systems strongly influence the predicted conversions. There is a need for experimental measurement of pKa for fatty acids in both water and alcohols at elevated temperatures.
1. INTRODUCTION Solvothermal processes use reactions in and with solvents (e.g., water, ethanol) at elevated temperatures and pressures. Processes using high temperature water (HTW) as a reaction medium for biofuel production from triglyceride (TG)-containing feedstocks include hydrolytic conversion of TGs in plant oils to fatty acids, green diesel or biodiesel feedstock,1,2 hydrothermal liquefaction of TG-rich wet algal biomass to produce crude bio-oils,3 hydrothermal carbonization of algae to produce biosolids,2,4 and supercritical water gasification of microalgal biomass.3,57 Processes that use high temperature alcohol as a reaction medium for biofuel production include the uncatalyzed reaction of fats, oils, or free fatty acids with the alcohol to produce fatty acid alkyl esters (biodiesel).812 Thus, an understanding of ester hydrolysis in HTW and fatty acid esterification in near- or supercritical alcohol is important for the development of several different potential biofuel processes. Moreover, for some of these biofuel processes, the fatty acid, ester, water, and alcohol will be simultaneously present. Therefore, it is important to understand the reactivity of this multicomponent system as it reacts from both the hydrolysis and esterification directions. These two reactions are really one, since each is the reverse of the other. The literature provides reports on the kinetics of TG and fatty acid ester hydrolysis and fatty acid (FA) esterification when each is studied in isolation.9,1320 Changi et al.21 have studied hydrolysis of ethyl oleate and esterification of oleic acid from 150 to 300 °C in tandem and proposed a phenomenological autocatalytic kinetics model, which gives good quantitative prediction of the conversion for either reaction. However, to the best of our knowledge, there have been no reports that provide mechanistic details. Clearly, an understanding of these reactions at the molecular level could prove beneficial for the biofuel production processes being developed. With this in mind, we report herein on the mechanism(s) for hydrolysis of fatty acid ester and esterification of the fatty acid, under solvothermal reaction conditions with no added catalyst. The mechanism then provides r 2011 American Chemical Society
a basis for a detailed chemical kinetics model that can be used to interpret, correlate, or predict experimental results. We develop the mechanism for ester hydrolysis and fatty acid esterification by drawing upon the literature, and we subsequently report experimental results that verify the mechanistic hypotheses. We discuss the mechanism for hydrolysis first and then the mechanism for esterification.
2. MECHANISMS FOR HYDROLYSIS Day and Ingold have classified hydrolysis of esters into eight possible mechanisms depending on whether the reaction is (1) acid- or base-catalyzed (A or B), (2) acyl or alkyl cleavage (ac or al), and (3) unimolecular or bimolecular (1 or 2), depending upon whether the carbocation (formed as an intermediate) transforms to the product by itself or by the addition of an alcohol molecule to it.22 Thus, the eight mechanisms that have been documented for esters (RCOOR0 ) are Aac1, Aac2, Aal1, Aal2, Bac1, Bac2, Bal1, and Bal2. This classification is a useful starting point, but it strictly applies to reactions with added acid or added base. The system in which we are interested involves no added catalystjust hydrolysis of TGs or fatty acid esters in neutral HTW. For acid catalyzed hydrolysis of esters, Aac2 is the most common mechanism. In the Aac2 mechanism, the first step is the protonation of the ester by H+ to generate a carbocation.22 The carbocation is subsequently attacked by a water molecule and, after a series of steps, forms the corresponding fatty acid and alcohol. Aal1 is the next common mechanism for esters having R0 that give stable carbocations. Aac1 is rare, being found mostly with strong acids and sterically hindered R. Aal2 is even rarer. For base-catalyzed hydrolysis, Bac2 is almost universal. Bal1 occurs only with R0 that give stable carbocations and only in weakly basic Received: June 24, 2011 Accepted: October 8, 2011 Revised: September 6, 2011 Published: October 12, 2011 12471
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Industrial & Engineering Chemistry Research or neutral solutions. Bal2 is very rare and Bac1 has never been observed. More details regarding these mechanisms can be found in the literature.22 There has been some previous mechanistic work on ester hydrolysis in near-neutral HTW, but none for long-chain fatty acid esters. Krammer and Vogel23 proposed a modified form of the Aac2 mechanism for hydrolysis of ethyl acetate in neutral HTW. They suggest that reaction of two water molecules with a protonated ester intermediate is the rate-determining step. The presence of two water molecules, possibly due to hydrogen bonding, differentiates their mechanism from the conventional Aac2 mechanism. All other steps following the rate-determining step were taken to be fast and irreversible. The authors developed a kinetics model from their mechanism, but they accounted for H+ arising only from the dissociation of the acetic acid product. Because no acetic acid is present initially, the reaction rate at t = 0 would be zero according to this model. In reality, H+ from the dissociation of water would be available at t = 0 to begin the reaction. Second, if the reaction is solely catalyzed by H+, as suggested by Krammer and Vogel23 then the pseudo-first-order rate constant, k, for reactant disappearance should be directly proportional to the hydronium ion concentration in the solution. More specifically the slope of log k plotted against the pH should be 1 for such a H+-catalyzed reaction. Krammer and Vogel23 did not check for this behavior by doing experiments at different initial pH values, but Comisar et al.24 have carried out pH studies for hydrolysis of methyl benzoate at 200 and 300 °C. Their results indicated a dependence of the pseudo-first-order rate constant on H+ much weaker than first-order in near neutral HTW. To account for their observations, Comisar et al.24 proposed a mechanism that included not only specific acid catalysis by H+ but also general acid catalysis by water molecules. They showed that such a mechanism led to a rate equation that was quantitatively consistent with experimental results. The kinetics become first order in H+ only at lower pH. Ravens25 also showed that very low pH (>3 N HCl) is needed to make ester hydrolysis specific acid catalyzed (for hydrolysis of polyethylene terephthalate fibers). Oka et al.26 proposed a base-catalyzed pathway for ester hydrolysis in supercritical water (SCW) because adding a protic acid did not alter hydrolysis rate of methyl 2-phenylpropionate at 390 °C. Oka et al.26 did not test their hypothesis by adding a base to the system, but given the findings of Comisar et al.,24 one expects little effect from either H+ or added OH in near neutral SCW. The experimental result from Oka et al.26 is consistent with the combination of general and specific acid catalysis proposed by Comisar et al.24 This review of the relevant literature indicates that ester hydrolysis can be catalyzed by H+, especially at very low pH and by water molecules especially at near-neutral pH. Moreover, it seems reasonable that if water can serve as a general acid catalyst, then the carboxylic acid formed by hydrolysis would be an even more effective general acid catalyst (although this hypothesis has not been previously tested). Thus, the mechanism we propose for hydrolysis of fatty acid alkyl esters includes catalysis by H+, by water, and by fatty acids. To our knowledge, this is the first account of general acid catalysis by fatty acids being considered.
3. MECHANISMS FOR ESTERIFICATION Following the mechanistic classification introduced by Day and Ingold for acid-catalyzed ester hydrolysis, four discrete mechanisms may be considered for esterification of fatty acids:
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reverse Aal1, reverse Aal2, reverse Aac1, and reverse Aac2.27 Note that the notations A, ac or al, and 1 or 2 mean the same as those mentioned for hydrolysis of esters in Section 2 and these mechanisms are the reverse of that for hydrolysis. The literature on mechanisms focuses on esterification at low temperatures with added acid2830 but esterification can take place without adding catalysts due to the weak acidity of the carboxylic acid reactant. The reaction is extremely slow at room temperatures, however, and requires several days to reach equilibrium.28 Other compounds, such as 2,6-diortho-substituted benzoic acids, follow reverse Aac1 and reverse Aal1 mechanisms because of steric hindrance. Straight-chain acids primarily follow the reverse Aac2 mechanism.22 In the reverse Aac2 mechanism, the first step is the protonation of the fatty acid by H+ to generate a carbocation.22 The carbocation is subsequently attacked by an alcohol molecule and, after a series of steps, forms the corresponding ester and water. Minami and Saka20 proposed a mechanism similar to Aac2 for esterification of fatty acids in supercritical methanol. The fatty acid reacts with a proton formed from the dissociation of the fatty acid. The carbocation then reacts with methanol to form an intermediate and water. This intermediate releases a proton and produces the ester in the final step. However, in their kinetics model they did not include the concentration of proton, which is an important parameter. The proton could come either from the dissociation of fatty acid or from the water, for systems with some amount of water initially present. Given the fact that the reverse of Aac2 mechanism is most likely for straight-chain esters, we use it as the most likely mechanism for our system. We note at this point that our embrace of the reverse Aac2 mechanism is tentative as the literature provides no direct support for any mechanism pertaining to esterification of fatty acid in high-temperature alcohol without added catalyst.
4. UNIFIED REACTION MECHANISM FOR HYDROLYSISESTERIFICATION The previous sections showed that the Aac2 mechanistic framework is the most likely option of fatty acid ester hydrolysis in HTW in the absence of added acid or base. We build on this foundation by noting that specific acid catalysis is probably not the sole mechanism for fatty acid ester hydrolysis. We include the possibility of general acid catalysis by water molecules, as proposed by Comisar et al.,24 and by the fatty acid hydrolysis product, which should be an even better proton donor than water. Figure 1 shows all the steps of the proposed mechanism. The forward reactions pertain to fatty acid ester hydrolysis, while the reverse reactions describe fatty acid esterification. Again, we emphasize that this mechanism is intended to describe hydrolysis and esterification in the absence of added mineral acid or base. In step a, oleic acid (the specific fatty acid used in this study) dissociates to give [H+] and [C17H33COO]. The dissociation constant (Ka) of the acid at the reaction conditions governs the formation of H+ ions. Step b shows the dissociation of water into H+ and OH, and the extent of this dissociation is quantified through the ion product of water, Kw. Ester hydrolysis is initiated by one of the parallel steps 13. We consider the possibility that the hydrolysis is catalyzed by H+ (step 1), obtained from dissociation of either fatty acid or water as shown in steps a and b, by oleic acid (step 2), and by water (step 3). 12472
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Figure 2. Schematic representation of hydrolysis and esterification mechanism.
Moreover, all steps are taken to be reversible. Equation 1 shows the rate equation. Note that ki and ki refer to the rate constants for the forward and reverse step i in Figure 1 and Ki refers to the ratio ki/ki. rEO ¼ rOA ¼
Qk7 CH þ CEtOH COA kb CW ðk1 CHþ CEO þ k2 COA CEO þ k3 CW CEO Þ kb CW þ Q ðCEtOH þ kc þ kd þ ke Þ
ð1Þ Q ¼ k3 COH þ k1 þ k2 CO kb ¼ k7 K4 K5 K6 , kd ¼
Figure 1. Mechanism for ethyl oleate hydrolysis and oleic acid esterification.
Steps 13 all generate the same protonated ester intermediate X1, which in step 4 adds a water molecule to produce another intermediate X2. In step 5, proton transfer takes place within the intermediate X2 to form intermediate X3, which then forms a carbocation X4 through the loss of ethanol in step 6. This carbocation subsequently forms the product oleic acid (OA) and regenerates H+, as shown in step 7. From the reverse reaction perspective, esterification starts with protonation of oleic acid (OA) in the reverse of step 7 to give a carbocation intermediate (X4), which is then attacked by ethanol to form intermediate (X3) in the reverse of step 6. This intermediate X3 undergoes rearrangement to give intermediate X2 in the reverse of step 5. In the reverse of step 4, water (W) is released to form a carbocation (X1). Intermediate X1 can subsequently form the product ester (EO) through the reverse of either the steps 1, 2, or 3. In the reverse of step 1, X1 forms ester and regenerates [H+]. In the reverse of step 2, X1 reacts with C17H33COO (denoted O in Figure 1) to produce ethyl oleate and oleic acid. In reverse of step 3, X1 reacts with OH to produce ethyl oleate and water. The reaction mechanism can be written in a simpler manner as shown in Figure 2. Note that the coreactants are written above the arrows for each step and the coproducts are written below the arrows.
5. REACTION RATE EQUATION The rate equation for ethyl oleate or oleic acid can be written analytically using the streamlined method outlined by Helfferich.31 The only assumptions made are that each step is an elementary reaction and that each intermediate is present in trace levels and in a quasi-stationary state. No assumptions need to be made regarding the identity or existence of any rate-determining steps.
k7 K6 , k5
kc ¼
ke ¼
ð2Þ
k7 , k6
k7 K6 K5 k4
ð3Þ
The rate equation given by eq 1 is more general and hence more complex than any previous rate equations considered for ester hydrolysis in near-neutral HTW.23,24 However, eq 1 reduces to the simple power-law form given by Krammer and Vogel23 if we incorporate their simplifying assumptions (step 4 is the rate-limiting step with two water molecules, steps 5, 6, and 7 are irreversible, and steps 2 and 3 do not occur). Equation 1 also simplifies to the form given by Comisar et al.24 when we incorporate their assumptions (step 2 does not occur).
6. KINETIC MODELING If the proposed mechanism is correct then the corresponding rate equation should be consistent with the experimental data. In this section, we develop a mechanistic kinetics model and fit it to experimental data to test for the consistency. The model will also provide insight into the rates of each step. The mechanistic kinetics model can be obtained (eq 5) by combining the rate equation (eq 1) with the design equation for a constant volume batch reactor (eq 4). dCi ¼ ri dt
ð4Þ
dCEO dC ¼ OA dt dt Qk7 CH þ CEtOH COA kb CW ðk1 CHþ CEO þ k2 COA CEO þ k3 CW CEO Þ ¼ kb CW þ Q ðCEtOH þ kc þ kd þ ke Þ
ð5Þ One can substitute expressions for concentration for each component (Ci) in terms of the conversion (X) of the limiting reactant, Ci = Ci0 (Ri + νiX) into eq 1, where Ri = initial molar ratio of component i to that of the limiting reactant and 12473
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vi = stoichiometric coefficient of component i, to obtain a differential equation that describes how conversion changes with the batch holding time for fatty acid ester (during hydrolysis) and fatty acid (during esterification). We assume that the rate constants and equilibrium constants follow Arrhenius/Van’t Hoff form (eq 6), where 10ai and Eai are the respective preexponential factor and activation energy. Eai ki ¼ 10ai exp ð6Þ RT The value of the dissociation constant of water Kw is temperature dependent and calculated using the correlation from Marshall and Franck.32 We found no literature values for Ka for oleic acid in water, ethanol, or ethanolwater mixtures at the temperatures of interest in this work. Therefore we treat Ka as an adjustable parameter. One expects the value of Ka to be different in water, ethanol, and waterethanol mixtures. On the basis of the experimental results of Rahman et al.33 for the Ka of saturated fatty acids in ethanolwater mixtures, we expect a linear relationship between log Ka and the mole fraction of ethanol. Therefore, we calculated the dissociation constant of oleic acid in ethanolwater mixture as the mole fraction weighted average of its value estimated in pure water (Ka,w) and pure ethanol (Ka,e), as shown in eq 7. log Ka ¼ x w log Ka, w þ x e log Ka, e
ð7Þ
where xe = 1 xw and xw is mole fraction of water. We numerically integrated the differential equations for hydrolysis and esterification using Euler’s method and simultaneously performed parameter estimation to determine numerical values for the various Arrhenius parameters. These calculations were performed using Microsoft Excel 2007 and its Solver function. The objective function to be minimized was the sum of the squared differences between the experimental and calculated conversions, from both hydrolysis and esterification experiments. We varied the size of the time step used in the numerical integration from 0.1 to 0.5 to 1 min and found that there was no difference in either the conversions or the estimated parameters. Thus, Euler’s method with a step size of 0.1 min was used as a suitable means of numerically integrating the differential equations. For hydrolysis, we used the data in Figure 1 and Table 1 of Changi et al.21 and for esterification we used the data reported in Figure 5 of Pinnarat and Savage9 and Table 2 and esterification data with added water from Table 3 of Changi et al.21 Using the methodology outlined above, we solved the kinetics model (eq 5) and obtained values of the Arrhenius parameters for the different collections of rate and equilibrium constants. The model results were largely insensitive to the precise numerical values for the Arrhenius parameters in k3, k3, kc, kd, and ke, and the numerical values of these parameters were very small (
